Wavelet modeling of contour deformations in Sobolev spaces for fitting and tracking applications

This paper proposes a new model for contour deformations using wavelets. This model uses Sobolev spaces to control the smoothness of the contour deformation. This formulation defines a probabilistic model that induces a prior distribution for contour deformation. Based on this distribution, the fitting problem is solved in Bayesian terms. The deformation model is also used to generate a prior dynamic model for contour evolution in time. This probabilistic model is then applied to solve the tracking problem. Computational results for several real-image problems are given for both the Kalman and condensation filters.     

Scalable Feature‐Preserving Irregular Mesh Coding

This paper presents a novel wavelet‐based transform and coding scheme for irregular meshes. The transform preserves geometric features at lower resolutions by adaptive vertex sampling and retriangulation, resulting in more accurate subsampling and better avoidance of smoothing and aliasing artefacts. By employing octree‐based coding techniques, the encoding of both connectivity and geometry information is decoupled from any mesh traversal order, and allows for exploiting the intra‐band statistical dependencies between wavelet coefficients. Improvements over the state of the art obtained by our approach are three‐fold: (1) improved rate–distortion performance over Wavemesh and IPR for both the Hausdorff and root mean square distances at low‐to‐mid‐range bitrates, most obvious when clear geometric features are present while remaining competitive for smooth, feature‐poor models; (2) improved rendering performance at any triangle budget, translating to a better quality for the same runtime memory footprint; (3) improved visual quality when applying similar limits to the bitrate or triangle budget, showing more pronounced improvements than rate–distortion curves.     

Front detection on satellite images based on wavelet and evidence theory: Application to the sea breeze fronts

This paper is concerned with the detection of fronts in satellite images. We focus on some specific textured patterns of clouds that are visible on Meteosat Second Generation (MSG) images and generated at the so-called “sea breeze front”. This is the limit of the penetration of the sea breeze inland. The sea breeze circulation is a phenomenon that arises when land and sea surface temperatures reveal strong variations. This generates a landward wind that creates a cloud-free area starting from the coast line and ending at the sea breeze front. With the new geostationary meteorological sensors like MSG, this band of cloud-free area can clearly be seen. The automatic analysis of the sea breeze front with such image sensors (instead of using local measurements) is then of great importance. It has the precious advantage to extract huge amount of data and to get rid of the use of local sensors. Unfortunately, from an image processing point of view, this front appears as the limit of a very textured area. It is sometimes disturbed by clouds located in higher layers of the atmosphere. Due to this complexity, conventional detection methods issued from computer vision are not adapted. In this paper we propose an approach that automatically detects fronts in images and we apply this framework to the sea breeze fronts. The methodology is based on the well-known active contour method (or “snake”) issued from the computer vision community. The specific textures involved as well as the transparency phenomena are dealt with some properties of the wavelet decomposition of the images. This decomposition enables to compute several criteria related to the presence or not of a front that are combined using the Dempster-Shafer theory. The validation of our approach is done on synthetic and real data. It is important to outline that the presented theoretical framework is not only devoted to the detection of the sea breeze front but can also be used to detect any others textured patterns.     

小波分析在钢丝绳无损检测中的应用

本文论述了采用漏磁通法检测钢丝绳局部损伤的原理和方法，并将小波理论有效地用于检测信号的处理中，用来确定局部损伤的位置，识别内外部断丝。     

Interest rate spreads and output: A time scale decomposition analysis using wavelets

The information content of several interest rate spreads for future output growth is analyzed using wavelet analysis. The “scale-by-scale” regression analysis shows that standard indicators of the stance of monetary policy, such as the shape of the yield curve, the real federal funds rate, and the credit spread have different information content for future output at different time frames. This is consistent with the idea that allowing for different time scales of variation in the data can provide a deeper understanding of the complex dynamics between real and financial variables, certainly richer than those obtainable using standard aggregate regression methods.     

Complex-Valued Wavelet Lifting and Applications

Signals with irregular sampling structures arise naturally in many fields. In applications such as spectral decomposition and nonparametric regression, classical methods often assume a regular sampling pattern, thus cannot be applied without prior data processing. This work proposes new complex-valued analysis techniques based on the wavelet lifting scheme that removes “one coefficient at a time.” Our proposed lifting transform can be applied directly to irregularly sampled data and is able to adapt to the signal(s)’ characteristics. As our new lifting scheme produces complex-valued wavelet coefficients, it provides an alternative to the Fourier transform for irregular designs, allowing phase or directional information to be represented. We discuss applications in bivariate time series analysis, where the complex-valued lifting construction allows for coherence and phase quantification. We also demonstrate the potential of this flexible methodology over real-valued analysis in the nonparametric regression context. Supplementary materials for this article are available online.     

Motion analysis in oceanographic satellite images using multiscale methods and the energy cascade

Motion analysis of complex signals is a particularly important and difficult topic, as classical Computer Vision and Image Processing methodologies, either based on some extended conservation hypothesis or regularity conditions, may show their inherent limitations. An important example of such signals are those coming from the remote sensing of the oceans. In those signals, the inherent complexities of the acquired phenomenon (a fluid in the regime of fully developed turbulence—FDT) are made even more fraught through the alterations coming from the acquisition process (sun glint, haze, missing data etc.). The importance of understanding and computing vector fields associated to motion in the oceans or in the atmosphere (e.g.: cloud motion) raises some fundamental questions and the need for derivating motion analysis and understanding algorithms that match the physical characteristics of the acquired signals. Among these questions, one of the most fundamental is to understand what classical methodologies (e.g.: such as the various implementations of the optical flow) are missing, and how their drawbacks can be mitigated. In this paper, we show that the fundamental problem of motion evaluation in complex and turbulent acquisitions can be tackled using new multiscale characterizations of transition fronts. The use of appropriate paradigms coming from Statistical Physics can be combined with some specific Signal Processing evaluation of the microcanonical cascade associated to turbulence. This leads to radically new methods for computing motion fields in these signals. These methods are first assessed on the results of a 3D oceanic circulation model, and then applied on real data.     

Fast interscale wavelet denoising of Poisson-corrupted images

We present a fast algorithm for image restoration in the presence of Poisson noise. Our approach is based on (1) the minimization of an unbiased estimate of the MSE for Poisson noise, (2) a linear parametrization of the denoising process and (3) the preservation of Poisson statistics across scales within the Haar DWT. The minimization of the MSE estimate is performed independently in each wavelet subband, but this is equivalent to a global image-domain MSE minimization, thanks to the orthogonality of Haar wavelets. This is an important difference with standard Poisson noise-removal methods, in particular those that rely on a non-linear preprocessing of the data to stabilize the variance.Our non-redundant interscale wavelet thresholding outperforms standard variance-stabilizing schemes, even when the latter are applied in a translation-invariant setting (cycle-spinning). It also achieves a quality similar to a state-of-the-art multiscale method that was specially developed for Poisson data. Considering that the computational complexity of our method is orders of magnitude lower, it is a very competitive alternative.The proposed approach is particularly promising in the context of low signal intensities and/or large data sets. This is illustrated experimentally with the denoising of low-count fluorescence micrographs of a biological sample.     

The circuit realization of Mexican Hat wavelet function

A wavelet network circuit implementation for Mexican Hat mother wavelet has been proposed for nonlinear function approximation which can also be used for the realization of the algebraic nonlinear components. The Mexican Hat mother wavelet function has been implemented with discrete circuit components and it has been observed that the experimental waveform obtained from the realized circuit is approximately same as the Spice simulation of the original function. The circuit simulations of exemplar functions implemented in Spice are also given.     

Subharmonic measurement using DFT and Wavelet-Packet Transform in an IEC extended framework

This paper proposes two different methods for measurement of subharmonic components in voltage and current waveforms in power systems. The paper first proposes a definition of the subharmonic group compatible with the standard of the International Electrotechnical Commission IEC 61000-4-7, as a grouping of spectral bins lower than the fundamental frequency resulting from the application of Discrete Fourier Transform. Then it presents a new method based on the Wavelet-Packet Transform to compute the magnitude of this subharmonic group. The performance of the two methods are compared in different measurement conditions.